According to distance measures accepted by standard astronomy, the answer is "very fast" or for distances beyond a light day (or closer) faster than the speed of light "by magnitudes". According to one of the two theories of relativity, that should be impossible.
Now, there is a problem with this. Knowing the distance to the stars.
Distances "within solar system" are all less than one light day off. Not even Pluto is with its accepted distance from us right now going around us at the speed of light. So, objects "within solar system" are not an issue.
And for Stars "outside the solar system", the distance measures are moot because the most fundamental are based on parallax.
That said, even if stars are just one light day away, either Einstein was wrong, or his principle does not apply to objects moving around us along with the aether. Or both.
Actually, it is less than a light day away that Einstein would run into this problem. A star distant 1 light day from us is each day making a tour of 2pi or 6.28 and some more light days. This means going 6-7 times faster than speed of light. If light has a finite speed and distance measures like light day or light year make sense. So, one object would be even closer, but still further away than Pluto, when Einstein started to object to Geocentrism on this ground. If he were around to object.